-CH.XIII.] MEASUREMENT OF PHENOMENA. 271 



cal power, a very precise instrument would be useless. 

 Measuring apparatus and mathematical theory should ad- 

 vance paripassu, and with just such precision as the theorist 

 can anticipate results, the experimentalist should be able 

 to compare them with experience. The scrupulously 

 accurate observations of Flamsteed were the proper 

 complement to the intense mathematical powers of 

 Newton. 



Every branch of knowledge commences with quantita- 

 tive notions of a very rude character. After we have far 

 progressed, it is often amusing to look back into the 

 infancy of the science, and contrast present with past 

 methods. At Greenwich Observatory in the present day, 

 the hundredth part of a second is not thought an in- 

 considerable portion of time. The ancient Chaldseana 

 recorded an eclipse to the nearest hour, and the early 

 Alexandrian astronomers thought it superfluous to dis- 

 tinguish between the edge and centre of the sun. By 

 the introduction of the astrolabe, Ptolemy and the later 

 Alexandrian astronomers could determine the places of 

 the heavenly bodies within about ten minutes of arc. 

 Little progress then ensued for thirteen centuries, until 

 Tycho Brahe made the first great step towards accuracy, 

 not only by employing better instruments, but even 

 more by ceasing to regard an instrument as correct. 

 Tycho, in fact, determined the errors of his instruments, 

 and corrected his observations. He also took notice 

 of the effects of atmospheric refraction, and succeeded 

 in attaining an accuracy often sixty times as great as 

 that of Ptolemy. Yet Tycho and Hevelius often erred 

 several minutes in the determination of a star's place, and 

 it was a great achievement of Ecemer and Flamsteed to 

 reduce this error to seconds. Bradley, the modern Hip- 

 parchus, carried on the improvement, his errors in right 

 ascension, according to Bessel, being under one second of 

 time, and those of declination under four seconds of arc. 

 In the present day the average error of a single observa- 

 tion is probably reduced to the half or quarter of what it 

 was in Bradley's time ; and further extreme accuracy is 

 attained by the multiplication of observations, and their 

 skilful combination according to the theory of error. 

 Some of the more important constants, for instance that 



